If Jn(x) represents the Bessel function of integer order n, then the derivative ddx[x-n Jn(x)] is given by:

Consider an antisymmetric tensor Pij with indices i and j running from 1 to 5. The number of independent components of this tensor is:

The Heaviside step function is defined as H(t) = 1 for t > 0 and H(t) = −1 for t < 0, and its Fourier transform is given by −2i/ω. The Fourier transform of 12[H(t + 1/2) − H(t − 1/2)] is: